Beach Day by Rodger Bliss
May 2024

Three Positive Numbers

Three Positive Numbers
What three positive numbers give the same result when multiplied and added together?

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8 guesses to Three Positive Numbers

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  • Frank, you are today’s winner!
    1, 2, and 3.

  • brent

    Looks like the square root of 3 would also solve this riddle if it is used as all three values.
    root 3 x root 3 x root 3 = root 3 + root 3 + root 3

    I don’t know how to tell if there are other solutions (other than the one Frank gave) where three unique values solve the problem? Any ideas?

  • brent

    O.K. I’ve found a general solution (but my inability to enter math formulae on here is a bit frustrating, I’m happy to follow-up if there is interest.

    But for example,
    If you assume A = square root of (11.1)
    Which is approximately 3.331666

    Then this is true:
    A/10 + A + Ax10 = A/10 x A x Ax10
    or approximately
    0.3331666 + 3.331666 + 33.31666 = 0.3331666 x 3.331666 x 33.31666 = 36.98149

  • brent

    For some reason, this one has captured me!

    Another three positive numbers that add up to their product are:
    (Where B = square root of 3.5)
    B/2 + B + 2B = B/2 x B x 2B

    Or approximately:
    0.935414 + 1.870829 + 3.741657 = 0.935414 x 1.870829 x 3.741657 = 6.5479

  • brent

    Oh boy, it is much easier than I had been making it out to be.

    Given any two positive numbers: B & C you can find the 3rd (usually smaller) number to complete the equation:
    A + B + C = A x B x C

    using: A = (B + C) / (B x C – 1)

    Of course, B x C – 1 must not equal 0.

    I think I can get on with my life now…